The Taliban took responsibility for Thursday's attack in Paktia province, calling it a “defensive action.”
Under a deal the U.S. signed with the Taliban in February, troop levels were to come down from about 12,000 to 8,600.
The government announced it would release 900 Taliban prisoners as a three-day cease-fire draws to an end.
President Ashraf Ghani said his administration was also ready to hold peace talks with the Taliban.
The Taliban offered a three-day truce over the Eid al-Fitr holiday.
The United Nations on Tuesday called for an immediate reduction of violence in Afghanistan.
The bomber reportedly used a stolen Humvee full of explosives, detonating it as he approached the main entrance gate.
The U.S. still plans to draw down 8,600 troops in Afghanistan by July.
A bombing in Paktia that looked to target a military compound but exploded before its destination killed five civilians.
While the battle was underway, Afghan security forces struggled to evacuate the facility.